Question

A solid uniform metal bar of diameter D and length L is hanging vertically from its upper end. The elongation of the bar due to self-weight is

• A. Proportional to L and inversely proportional to $D^2$
• B. Proportional to $L^2$ and inversely proportional to $D^2$
• C. Proportional to L and independent to D
• D. Proportional to D and inversely proportional to $L^2$

Hint:

Always pay attention to whether "weight" or "density" is treated as the independent constant.
If weight $W$ is constant, $\delta \propto \frac{L}{D^2}$. If density $\rho$ is constant, $\delta \propto L^2$ and is independent of $D$.

Answer 1

The Correct Option is A